prove that the equation
Z^3 + 2Z +4=0
has no roots in the circle uint.
thanks.

Unit circle would mean that you can express your solutions as
Thus,
Using De'Moiver's Theorem,
Thus, (by definition of complex number equality)
But the first equality cannot hold because the minimum cosine is at -1. Thus, even if it were to be at -1 then, its value would be
Thus, the first equation the LHS is greater than the RHS-impossible.